The mathematics of the human menstrual cycle are remarkably understudied. Although several hundred biological papers are written on the topic every year, there is no established mathematical model for the cycle, and there have been only about a dozen mathematical papers addressing the subject in the past 30 years. Almost all of these mathematical papers are over 10 years old, and are thus physiologically out of date. The mathematics of the menstrual cycle is therefore a wide open topic, with a wealth of medical applications, from ovarian and breast cancer, to polycystic ovarian syndrome, infertility treatments, and passage to menopause. The long-term goal of this project is to develop a realistic, quantitative model of the neuroendocrine control of the menstrual cycle, in order to make computational predictions about the impact of different hormonal environments on the cycle. We propose to use mathematics, and nonlinear dynamical systems in particular, to analyze the available experimental data in the high dimensional settings required to simultaneously keep track of the hormone interactions at varying time scales. Our approach to the project is three-fold: First: develop physiologically based models of pulsatile LH and GnRH release from populations of secretory cells, mimicking the electrical and chemical communication within and between the cell populations in the hypothalamus and pituitary. Use the GnRH model to drive the LH model while the ovarian hormones modulate the intrinsic frequencies of both models. Analyze the coupled system for transient resonance phenomena modeling the LH surge. Second: generalize the classical work of Lacker et. al. to develop a model of the competitive dynamics among a cohort of ovarian follicles that is consistent with data from normally cycling women; women with infertility conditions such as polycysic ovarian syndrome (PCO), and women undergoing fertility treatment. Finally: adapt the menstrual cycle model of Selgrade and Schlosser to incorporate these physiological driven sub-models. At each stage of the modeling process we will compare and validate the model with experimental data collected from the literature, experimentalists and fertility clinics.